Multipole expansions in four-dimensional hyperspherical harmonics

The technique of vector differentiation is applied to the problem of the derivation of multipole expansions in four-dimensional space. Explicit expressions for the multipole expansion of the function r^n C_j (\hr) with \vvr=\vvr_1+\vvr_2 are given in terms of tensor products of two hyperspherical harmonics depending on the unit vectors \hr_1 and \hr_2. The multipole decomposition of the function (\vvr_1 \cdot \vvr_2)^n is also derived. The proposed method can be easily generalised to the case of the space with dimensionality larger than four. Several explicit expressions for the four-dimensional Clebsch-Gordan coefficients with particular values of parameters are presented in the closed form.Comment: 19 pages, no figure

One-loop self-energy correction in a strong binding field

A new scheme for the numerical evaluation of the one-loop self-energy correction to all orders in Z \alpha is presented. The scheme proposed inherits the attractive features of the standard potential-expansion method but yields a partial-wave expansion that converges more rapidly than in the other methods reported in the literature.Comment: 8 pages, 4 table

QED calculation of the 2p3/2-2p1/2 transition energy in five-electron ion of argon

We perform ab initio QED calculation of the (1s)^2(2s)^22p_{3/2} - (1s)^2(2s)^22p_{1/2} transition energy in the five-electron ion of argon. The calculation is carried out by perturbation theory starting with an effective screening potential approximation. Four different types of the screening potentials are considered. The rigorous QED calculations of the two lowest-order QED and electron-correlation effects are combined with approximate evaluations of the third- and higher-order electron-correlation contributions. The theoretical value for the wavelength obtained amounts to 441.261(70) (nm, air) and perfectly agrees with the experimental one, 441.2559(1) (nm, air).Comment: 10 pages, 3 figures, 1 tabl

Optical Lattice Polarization Effects on Hyperpolarizability of Atomic Clock Transitions

The light-induced frequency shift due to the hyperpolarizability (i.e. terms of second-order in intensity) is studied for a forbidden optical transition, $J$=0$\to$$J$=0. A simple universal dependence on the field ellipticity is obtained. This result allows minimization of the second-order light shift with respect to the field polarization for optical lattices operating at a magic wavelength (at which the first-order shift vanishes). We show the possibility for the existence of a magic elliptical polarization, for which the second-order frequency shift vanishes. The optimal polarization of the lattice field can be either linear, circular or magic elliptical. The obtained results could improve the accuracy of lattice-based atomic clocks.Comment: 4 pages, RevTeX4, 2 eps fig

Parametrizations and dynamical analysis of angle-integrated cross sections for double photoionization including nondipole effects

Similarly to differential cross sections for one-electron photoionization, the doubly differential cross section for double photoionization (DPI) may be conveniently described by four parameters: the singly differential (with respect to energy sharing) cross section (σ0), the dipole asymmetry parameter (β), and two nondipole asymmetry parameters (Y and δ). Here we derive two model-independent representations for these parameters for DPI from a S01 atomic bound state: (i) in terms of one-dimensional integrals of the polarization-invariant DPI amplitudes and (ii) in terms of the exact two-electron reduced matrix elements. For DPI of He at excess energies, Eexc, of 100 eV, 450 eV, and 1 keV, we present numerical results for the asymmetry parameters within the framework of the convergent close-coupling theory and compare them with results of lowest-order (in the interelectron interaction) perturbation theory (LOPT). The results for Eexc=1keV exhibit a nondipole asymmetry that is large enough to be easily measured experimentally. We find excellent agreement between our LOPT results and other theoretical predictions and experimental data for total cross sections and ratios of double to single ionization cross sections for K-shell DPI from several multielectron atoms

Rescattering effects in laser-assisted electron-atom bremsstrahlung

Rescattering effects in nonresonant spontaneous laser-assisted electron-atom bremsstrahlung (LABrS) are analyzed within the framework of time-dependent effective-range (TDER) theory. It is shown that high energy LABrS spectra exhibit rescattering plateau structures that are similar to those that are well-known in strong field laser-induced processes as well as those that have been predicted theoretically in laser-assisted collision processes. In the limit of a low-frequency laser field, an analytic description of LABrS is obtained from a rigorous quantum analysis of the exact TDER results for the LABrS amplitude. This amplitude is represented as a sum of factorized terms involving three factors, each having a clear physical meaning. The first two factors are the exact field-free amplitudes for electron-atom bremsstrahlung and for electron-atom scattering, and the third factor describes free electron motion in the laser field along a closed trajectory between the first (scattering) and second (rescattering) collision events. Finally, a generalization of these TDER results to the case of LABrS in a Coulomb field is discussed

Ground-state hyperfine structure of H-, Li-, and B-like ions in middle-Z region

The hyperfine splitting of the ground state of H-, Li-, and B-like ions is investigated in details within the range of nuclear numbers Z = 7-28. The rigorous QED approach together with the large-scale configuration-interaction Dirac-Fock-Sturm method are employed for the evaluation of the interelectronic-interaction contributions of first and higher orders in 1/Z. The screened QED corrections are evaluated to all orders in (\alpha Z) utilizing an effective potential approach. The influence of nuclear magnetization distribution is taken into account within the single-particle nuclear model. The specific differences between the hyperfine-structure level shifts of H- and Li-like ions, where the uncertainties associated with the nuclear structure corrections are significantly reduced, are also calculated.Comment: 22 pages, 11 tables, 2 figure

Weak-Light Ultraslow Vector Optical Solitons via Electromagnetically Induced Transparency

We propose a scheme to generate temporal vector optical solitons in a lifetime broadened five-state atomic medium via electromagnetically induced transparency. We show that this scheme, which is fundamentally different from the passive one by using optical fibers, is capable of achieving distortion-free vector optical solitons with ultraslow propagating velocity under very weak drive conditions. We demonstrate both analytically and numerically that it is easy to realize Manakov temporal vector solitons by actively manipulating the dispersion and self- and cross-phase modulation effects of the system.Comment: 4 pages, 4 figure

Development of cross-border tourist and recreational regions on the Karelian section of the Russian-Finnish border

Despite that fact that cross-border tourism and recreation in the Baltic Sea Region have been extensively studied, there are still areas, which require further research. The aim of this article is to identify regions having active cross-border tourism and recreation in the adjacent territories of Finland and the Republic of Karelia. The authors propose to use an indicator characterizing the volume of incoming tourist flows. The number of tourists is not only indicative of the development of cross-border tourism and recreation; it is also one of the main criteria for determining the degree of the formation of cross-border regions. Using the statistics for Finland, the authors analyzed the geography of tourism in Finland's border areas and identified the degree of intensity of cross-border tourism exchange between the neighbouring administrative units of the two countries. The article also examines other tendencies indicative of the formation and development of cross-border tourism and recreation regions along the Russian-Finnish border. The authors identified three cross-border tourism and recreation regions of different development levels: South Karelia, Middle Karelia and North Karelia. South Karelia is a mesoregion with the average annual tourist exchange of about 100 thousand people, which is the average level of tourism development. The total volume of cross-border tourist flows from and to other cross-border tourist and recreation regions is about 30 thousand people per year. Middle Karelia microregion ranks second and is followed by the North Karelian microregion. The authors conclude that these two microregions are at the initial stage of their formation and, therefore, can be regarded as parts of one microregion - Russian-Finnish Northern microregion

AC Stark shift of the Cs microwave atomic clock transitions

We analyze the AC Stark shift of the Cs microwave atomic clock transition theoretically and experimentally. Theoretical and experimental data are in a good agreement with each other. Results indicate the absence of a magic wavelength at which there would be no differential shift of the clock states having zero projections of the total angular momentum